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http://www.cambridge.org/9780521875653

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interference is experienced are passed through. The nulls can be very

deep. At a particular distance (known as the ‘break point’) the oscil-

lation in signal strength ceases. This is because the angle between the

direct and reflected rays becomes so small that the first maximum is

always above the height of the receiving antenna. As the distance

increases further, the height of the first maximum continues to increase

and the height of the antenna represents a smaller fraction of the dis-

tance from the ground to the maximum. Thus, as distance increases,

two factors (free-space loss and the field strength at a fixed height

representing a smaller fraction of the field strength at a maximum)

combine to accelerate the increase of path loss with distance. The result

is that the signal strength reduces faster than it does before the break

point. At distances less than the break point the signal reduces with

free-space loss but experiences both constructive and destructive

interference so that the general trend of reduction in signal strength

with distance follows a 20 log(distance) line. This trend is shown as a

dashed line in figure 4.6 for distances less than 10 km. Beyond the break

–60

–40

–20

0

1 10 100

Distance (km)

R
e
la

ti
v
e
s

ig
n

a
l

st
re

n
g

th
(

d
B

)

Figure 4.6 The variation of signal strength with distance over a smooth reflecting

plane for transmitter and receiver heights of 40 m at a frequency of 500 MHz.

propagation over a flat plane 93

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point at 10 km the signal strength will reduce not only as the free-space

loss increases but also because the antenna is increasingly at a point of

destructive interference. This causes the reduction in signal strength with

distance beyond the break point to follow a trend closer to 40 log(dis-

tance). The dashed line in figure 4.6 shows indicates a 40 log(distance)

slope at distances between 10 km and 100 km. If the height of the

receiving antenna is increased to 80 metres, the distance to the break

point also doubles, to 20 km, as indicated in figure 4.7.

If the frequency is reduced then the break point reduces proportionately.

The distance to the break point can be estimated by using the equation

break point ¼ 4h1h2
k

, ð4:7Þ

where h1 and h2 are the heights of the transmitting and receiving

antennas, respectively, and k is the wavelength. The equation is in ‘self-

consistent’ units, meaning that, if the input parameters are all in metres,

the result will also be in metres.

–60

–40

–20

0

10 100

Distance (km)

R
e
la

ti
v
e
s

ig
n

a
l
st

re
n

g
th

(
d

B
)

1

Figure 4.7 Signal strength against distance for a receiver height of 80 metres.

reflection, scatter and penetration94

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Index

antenna beamwidth 2, 5, 9, 25

antenna feeder 21

antenna gain 2, 5, 6

antenna height 31

aperture antenna 2, 5, 16

aperture efficiency 8, 12

array of two half-wave dipoles 40

atmospheric absorption 141–2

atmospheric effects 10, 24, 116–49

base stations 26

base-station antennas 38–46

basic transmission loss 2

bit error ratio 15, 16

Boltzmann’s constant 15, 17, 157

system design 163–6

television 28

transmitters 26

building penetration 36

clearance requirements 61, 79

clutter 27

comparison between propagation at 900MHz

and propagation at 1800 MHz 37–8

Cornu spiral 53, 56, 57, 59, 101

COST action 36, 130–2

coverage area 28

quick check 35, 36

decibel scale 185–7

diffraction 50

Bullington method 71, 76

by practical obstacles 78

Deygout method 71, 72

diffraction loss 51

Epstein–Petersen method 71 , 72

geometric theory 78–9

grazing incidence 51

knife-edge 50–61, 113

multiple knife-edge prediction methods

50, 70–8

through an aperture

uniform theory 71

dipole antenna 26

directivity 4

diversity 96, 125–30

angle diversity 129

frequency diversity 127

in mobile communications 130

polarisation diversity 129

space diversity 95, 96, 126

ducting 117–18, 135–8

Earth bulge 119, 155

effect of frequency 33

effect of obstacles

effective aperture 4, 5, 7

electric field strength 26, 28, 29

converting from field strength to received

signal power 30

electrical down-tilt

electromagnetic wave 28

18, 26, 36

folded dipole 39

free-space loss 2, 11, 12

Fresnel integral 59

Fresnel parameter 51, 52, 58, 59

Fresnel zones 79, 155

geostationary satellite 17

GSM antenna 42

half-wave dipole 38

Huygens’ principle 53, 68

200

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in-building systems 170–1

interference 15, 26, 47

and the noise floor 47

reduction in coverage range 47

pattern 88

prevention 159–61

intrinsic impedance of free space 29

isotropic antennas 1, 3, 7

transmission loss between 11

ITU recommendation P. 530 120

ITU recommendation P. 1546 28, 31

k-factor 118–20
knife-edge obstacle 50

licensing and assignment 159–61

Maxwell’s equations 75

mobile communications 25, 26

mobile station antennas 46

mobile terminal 27

multipath propagation 116–17

near-field effects 18–24

noise 145–8

noise temperature 15

on Earth–space systems 146–8

Okumura–Hata 35–7, 45, 46
omni-directional antenna 26

parabolic equation 75

penetration of materials 85, 106–8

phasor diagrams 251

point-to-area transmission 26–49

point-to-point transmission 10–18, 153–63

polarisation 24–5

horizontal, 24

circular, 24

vertical, 24

power density 3, 5, 13, 21, 26, 28, 29

predicting field strength at a distance 31

principal direction 5

propagation over a flat plane 92–4

break point 93

propagation over water 95–8

quality of service 48

for an eight-element collinear array 42

of an aperture antenna 67

side lobes 67, 69

reflection 163

from a finite surface 64–7

from rough surfaces 101–6

reflection coefficient 67, 83, 90–1

required receive signal power 10, 14, 48

rain attenuation 138–41

Rayleigh criterion 104, 106

Rayleigh environment 83, 98–101, 111

Rician environment 83, 98–101, 111

satellite Earth station 15

scatter 84

sectored antenna 27, 43–6

gain 46

hexagonal coverage pattern 45

standing wave pattern 84, 85–90

thermal noise 47

transmission loss between practical

antennas 12

uniform plane wave 51

visible horizon 33

Walfisch–Ikegami 35, 37

wave front 87

wavelets 53, 55

index 201